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Abstract

Numerical simulations of small, utility scale wind turbine groupings were performed to determine how wakes generated by upstream turbines affect the performance of the small turbine group as a whole. Specifically, various wind turbine arrangements were simulated to better understand how turbine location influences small group wake interactions. The minimization of power losses due to wake interactions certainly plays a significant role in the optimization of wind farms. Since wind turbines extract kinetic energy from the wind, the air passing through a wind turbine decreases in velocity, and turbines downstream of the initial turbine experience flows of lower energy, resulting in reduced power output. This study proposes two arrangements of turbines that could generate more power by exploiting the momentum of the wind to increase velocity at downstream turbines, while maintaining low wake interactions at the same time. Simulations using Computational Fluid Dynamics are used to obtain results much more quickly than methods requiring wind tunnel models or a large scale experimental test.

Keywords

Turbine; Kinetic energy; Upstream and downstream

Introduction

Wind energy is a growing source of alternative power in many
countries around the world. With many advantages, including a cost
per kilowatt hour equivalent to that of an average coal power plant
(2.5-3.5 ¢/kWh), wind energy has established itself as an affordable
and stable competitor in the energy production market [1]. The earliest
recorded machines that harnessed the powter of the wind are the grain
grinding mills in Persia [2]. When European travelers and crusaders
discovered this technology and brought it to Europe, the transfer of
concepts eventually led to the trademark "Dutch" windmill designs,
often used to draw water from the ground or grind grain. With the
advent of electricity, the next logical evolution in wind power was
the wind turbine, which directly converts the kinetic energy of the
wind to electricity. A major figure in advancing windmills to create
wind turbines in 1891 was the Danish scientist Poul La Cour [3].
In the twentieth century, several countries produced variations of
the horizontal axis wind turbine (HAWT) in attempts to create more
efficient designs. Compared to drag based designs, these lift based
turbines are far more efficient. Even as small scale wind power was
experiencing a decline during the 1930s, continued advancements were
made in larger scale wind energy generation. In 1941, the collaboration
between American engineer Palmer C. Putnam and the Morgan Smith
Company of York, Pennsylvania produced the largest wind turbine in
the world. This turbine, capable of producing 1.25 MW, would hold
that record for almost 40 years. Putnam's goal when designing this
turbine was to create a turbine that would be able to produce energy at
a rate competitive with common power production methods [4]. It is
with this same goal that many utility scale wind turbines are designed
today. By 2008 the United States had an estimated capacity of 25000
MW of wind energy. By 2030, the U.S. hopes to use wind power for
20% of its electrical generation requirements [5]. Because of this, there
is a considerable need for research dedicated towards the improvement
of wind turbine and farm efficiency.

Available wind energy is a significant issue in wind farm
arrangement. Because a 1.0 m/s decrease (from 10 m/s to 9 m/s) in wind
velocity can result in a 25% drop in power output for a given turbine,
it is crucial to site wind turbines such that turbines upstream will not
adversely affect the overall performance of the farm. The reduction of
available wind power within a farm is usually referred to as a wake or array effect. Since kinetic energy is extracted by each turbine, the air
flow exiting a turbine contains less energy for a downstream turbine to
extract. By accounting for this effect, a wind farm operator can more
accurately decide where to place turbines within a farm to improve
energy output. Maintenance costs can also be reduced by accounting
for the wake effect, since wakes generated by turbines often induce
wind flow outside of ideal design parameters [4].

Wind turbine manufacturers continue to reduce the cost of
wind turbines and improve their operating efficiencies, and over the
past several decades, the reliability and efficiency of wind turbines
have improved greatly. Better wind turbines, in conjunction with a
reduction of the overhead costs associated with installing a wind farm
and government tax incentives for operations have made wind power
more enticing than ever [5]. However, in order to provide electricity at
a price that remains competitive with other power production methods,
ongoing research within the field of wind energy must be pursued.

Of great importance is the aerodynamic performance of HAWTs.
Hansen and Butterfield [6] discussed the research on the aerodynamics
of wind turbines and some popular methods of analyzing aerodynamic
performance. At the time, the most popular technique for the macro
scale analysis of rotors involved Blade Element Momentum (BEM)
theory. Due to its ease of use, as well as its accuracy, the BEM
method was one of the most widely used methods for examining the
flow physics of wind turbine rotors during the end of the twentieth
century, and it continued to be the basis for almost all rotor design
codes during the past decade [6-9]. While the BEM method provides
a ballpark estimation of a rotor's performance, wind tunnel testing is
still more accurate at predicting overall power output due to the BEM method's assumptions regarding complex flow phenomena. Though
modifications of the BEM method have been attempted, the inherent
assumptions that form the basis of this method's calculations limit its
overall accuracy [10].

Combinations of BEM based techniques with the more complex
full Navier-Stokes equations are typically more successful than pure
modifications of the technique in terms of accuracy. In 2002, Sørensen
and Shen [11] developed an aerodynamic model for examining the
three dimensional flow field surrounding a wind turbine. The model
they developed employs a combination of the three dimensional
Navier-Stokes equations and the actuator line technique. Using
this technique, they validated the model by performing an analysis
of a three bladed 500 kW HAWT. While the BEM methods remain
popular for calculating rotor loads and performance, in order to create
an accurate depiction of unsteady flow physics, dynamic loading,
and other complicated flow physics, more sophisticated methods for
examining forces on rotors are needed.

Vortex wake methods have been applied with varying degrees
of success to the analysis of wind turbines. Oftentimes, vortex wake
methods are implemented into existing analysis models. AeroDyn
is currently one of the most popular models for wind turbine design
and analysis in the United States. It functions by using a combination
of the BEM theories and a simplified variation of the vortex wake
methods. However, while fairly accurate, it still lacks the ability to
provide complete aerodynamic results, leading to attempts to combine
the accuracy of vortex wake models with the speed of AeroDyn [12].
Hugh D. Currin, Frank N. Coton, and Byard Wood [13,14] have
developed and validated a new wake model for the analysis of HAWTs.
The prescribed vortex wake code HAWTDAWG, developed at the
University of Glasgow, was linked to AeroDyn and the structural
dynamics code FAST in an effort to provide greater accuracy under
dynamic flow conditions. The results obtained from this study were
compared to experimental Phase VI wind tunnel data, as well as to basic
BEM and vortex wake methods built into AeroDyn. HAWTDAWG
produced results comparable to both the experimental data and the
BEM methods during steady, axial flow.

The most accurate numerical method for analysis of fluid flow is
directly solving the Navier-Stokes equations governing fluid motion.
This is the underlying basis of Computational Fluid Dynamics (CFD).
While there are projects geared towards improving currently existing
models, with the ever-increasing power of computational systems,
using CFD to calculate results based on the Reynolds Averaged Navier-
Stokes (RANS) equations has proven to be both accurate and efficient.
In 2002, Sørensen et al. [15] completed a RANS simulation of the
NREL Phase VI Rotor. The calculated results from this simulation
were in good agreement with both BEM methods previously used to
model the rotor, as well as with experimental measurements made
in the NASA Ames wind tunnel. This simulation also proved that
accurate aerodynamic results could be obtained from a 3D CFD
simulation. While CFD is more computationally costly than any of the
aforementioned methods of analysis, due to advances in modern day
computing, CFD is becoming a popular method for analysis when large
amounts of detail are required [16].

Currently, there are two major methods of applying CFD for wind
turbine analysis. To analyze a given problem, either a commercially
available solver can be used or new code can be written and applied.
In this project, due to its ease of use and availability, the commercially
available CFD package ANSYS Fluent® is used. Various research projects
have been conducted using commercial CFD codes, many of which have performed additional validation studies supporting the accuracy
of commercial software. One of the most common commercial CFD
codes, ANSYS Fluent® is used in many projects due to its flexibility
and accuracy. Amano et al. [17] used Fluent® to analyze and improve
the design of a wind turbine rotor blade, resulting in the addition of
a swept edge to the blade in an effort to extract greater amounts of
power from the wind. Palm et al. [18] used Fluent® to determine basic
relations that can be used to predict the power output of a given tidal
farm configuration.

In 2007, Wußow et al. [19] used ANSYS Fluent® to model a fullsized
wind turbine and determine the aerodynamic flow physics in the
wake downstream of the rotor. By using a direct model with a body
fitted grid, this simulation aimed to accurately capture the flow physics
generated by the interaction of rotating turbine blades with a given
wind flow. In this case, the rotor rotational speed was fixed at a value
corresponding to the velocity of the oncoming wind at the wind turbine
hub height. Although this assumption reduces the computational time
required for the simulation, it prevents aerodynamic forces from being
accurately modeled on the wind turbine rotor. However, this does not
affect the downstream wake aerodynamics, which is the main focus
of the project. Using the Large Eddy Simulation (LES) turbulence
model, Wußow et al. generated results that matched experimental data
closely, albeit representing only the lower range of available data. Thus,
simplified CFD simulations can provide accurate results in the small
time frames encountered in many industrial settings [20].

Several other commercial CFD software packages exist, including
ANSYS CFX. CFX was applied by McStravick et al. [21] to analyze the
Eppler 423 airfoil as a wind turbine blade. The domain was designed to
contain only one blade with periodic boundary conditions to simulate
the full turbine. While these other CFD packages exist and have been
applied to the analysis of many types of simulations, the popularity and
dependability of ANSYS Fluent® make it ideal for the current study.

Objectives

The primary objective of this project is to complete numerical
simulations of utility scale wind turbines in two major arrangements
designed to optimize energy extraction and decrease the effect of
wake losses. From these simulations, the flow physics surrounding
the rotors of multiple turbines will be examined. Also, interactions
between wind turbines within the simulated wind farms will
be examined to determine the effect wakes have on the energy
production potential of the proposed siting arrangements.
Three major wind farm arrangements will be simulated in this project.
The first is a common space saving arrangement. By placing wind
turbines in small rows, typically groups of three to five turbines, space
is conserved. However, by placing turbines this close to one another,
large losses may be induced by wakes. Simulations of this geometry will
be used as the baseline.

The second arrangement uses groups of triangularly spaced
turbines. As wind passes through a turbine, some of the air cascade
around the sides of the turbine. The air passing around the turbine is
then forced into the freestream air flow, slightly accelerating the fluid
passing around the turbine. By locating turbines in triangular groups,
with two turbines placed relatively close downstream and to the left
and right sides of the upstream turbine, it is hypothesized that the
downstream turbines will be able to generate more power.

The third arrangement is essentially a reversed triangular pattern,
or a "delta." The delta simulations are designed to determine if an increase in velocity in a single turbine downstream of two turbines
results in a larger overall increase in power than seen in the triangular
arrangement. The project will also attempt to determine any adverse
issues with the triangular and delta arrangements by examining various
angles of wind flow, as well as the spacing of turbines within a given
area. In all of the aforementioned turbine arrangements, the turbines
are placed on a flat surface for simulation, similar to a level field with
very few trees, or an offshore wind turbine farm.

Theory

CFD numerically solves the complex PDEs known as the Navier-
Stokes equations, which govern fluid flow, by discretizing them into a
simpler system of algebraic equations that can be easily calculated at
various points within a fluid domain. A major concern when analyzing
any flow field with CFD is the accuracy of the simulation. Not only can
computers introduce rounding errors, results generated by CFD can
only be as accurate as the physical models developed to represent fluid
flow. Nonetheless, CFD has proven to be an extremely accurate tool for
predicting fluid flow in an extremely broad spectrum of applications,
including the simulation of wind energy aerodynamics [22].

The simulations performed in this study are run as steady state
cases using SIMPLE pressure-velocity coupling. The following
methods are used for spatial discretization: 1) least squares cell based
gradients, 2) Fluent® standard pressure discretization, and 3) the second
order upwind method for momentum, turbulent kinetic energy, and
specific dissipation rate. A brief comparison of the wakes generated
by transient simulations with those observed in the steady state model
was conducted early on in the project. The differences observed in
wake formulation are mostly limited to increased vortex generation
and vorticity in the wake, with minor variations in velocity. In order
to optimize the computational efficiency of the simulations, the steady
state model was selected over transient models. Initialization of all
cases was performed using Fluent’s® hybrid initialization scheme,
which solves the Laplace equation to produce an initial velocity field
compliant with the boundary domains and cell zone conditions.

Several of the available turbulence models were considered for use
in this project, including the Standard k-ε model, the k-ω and k-ω SST
models, and more complex models such as the Large Eddy Simulation
(LES) and Detached Eddy Simulation (DES) models. The k-ω SST
(shear stress transport) model combines the near-wall/vortex accuracy
of the k-ω model with the freestream accuracy of the k-ε model. This
results in a turbulence approximation model capable of accurately
representing the flow physics at the boundary layers surrounding the
wind turbine blades, as well as the size, shape, and intensity of the wake
as it travels downstream of the turbine.

The LES and DES methods were also examined for use in this
project. However, since LES and DES simulations are typically run as
transient simulations, they require extremely large computation times.
Since the results (size, shape, and position of the turbine wakes) from
LES and DES methods differ little from the results from the k-ω SST
turbulence model during low turbulence flows, it seems clear that the
k-ω SST model is best suited for the simulations in this project [23].
The equations for the k-ω and k-ω SST models are as follows:

Equation for k:

Equation for ω:

Numerical Methodology

The design of the wind turbine in this study is based on GE's 1.5
MW utility scale turbines, shown in Figure 1. Since its properties and
dimensions are publicly available, this project is able to simulate utility
scale wind turbines under realistic operating conditions without the
need for proprietary information.

Figure 1: GE’s 1.5 MW turbines [24].

The size, scale, and general operating conditions of this turbine
class are available on GE Energy's website.

The blades are based on the popular NREL S809 airfoil with
decreasing chord length. The detailed blade design is shown in Figure 2.
The blade is also twisted along its length by 22 degrees. A preprocessing
software (Gambit®) was used to generate the simulation mesh.

Figure 2: S809 Airfoil [25].

Using this blade design, a three-bladed HAWT is created by
attaching the blades to a basic hub and nacelle geometry with a 77
m tower. For each domain, a mesh of roughly 13.5 million cells is
generated. The simulations are performed using a rectangular box
domain 1.5 km in length, 1 km in height, and 1.5 km in width, with a
velocity inlet, pressure outlet, and fixed ground. To simulate the rotor
assembly under operating conditions, a cylindrical sliding mesh zone 80
meters in diameter is created surrounding the turbine rotor. This zone
is meshed independently of the external flow domain and consists of
roughly 1.5 million cells. The cell size near the turbine rotor is specified
to be 0.1 meters, expanding at a growth rate of two to 0.5 meters at the
outer interfaces. The remaining domain mesh quality is controlled by
blocking the domain. The turbine is surrounded by a cube 150 meters
per side and the cell size at the turbine tower and nacelle is also specified
to be 0.5 meters. The mesh is allowed to expand to a maximum cell size of 3.5 meters within this zone. Any turbines are then surrounded
by a flow block 500 meters wide by 200 meters tall, with a maximum
cell size of 7 meters traversing the length of the domain from inlet to
outlet. Finally, the remaining domain is meshed as a farfield zone with
a maximum cell size of 17 meters. Figure 3 showcases the 3D model of
the turbine and the flow domain for simulation.

Figure 3: Final wind turbine geometry (left) and an example of a turbine
arrangement with domain blocking for mesh design (right).

The next step in creating the geometry is to define the boundary
conditions. Boundary conditions define various fluid properties at
certain locations within the domain. In this case, since a uniform
freestream velocity over the wind turbines of 12 m/s is desired, the
velocity inlet boundary condition is set at the inlet face of the domain’s
large boundary box. This inlet can be set to any given velocity, and it
can be varied from case to case. The base simulation inlet speed is 12
m/s, with a turbulent intensity of 5%, and a turbulence length of one
meter. The domain outlet is set at the back face of the boundary domain
and is defined as a pressure outlet with the pressure at one atmosphere.

The walls and ground of the boundary domain are simple no-slip
walls. However, in order to remove the boundary layer on the side and
top walls during steady state simulations, they are set to have a constant
translational velocity equal to that of the freestream. Therefore, in the
base case, the side and top walls move at 12 m/s. This eliminates the
wall boundary layer and allows for unimpeded freestream flow.

The wind turbine blades, tower, and nacelle are all basic wall
boundary conditions with the no-slip condition, and the volumes
are set to specific fluid cell zones. Every volume except the cylindrical
volumes surrounding the wind turbine rotor assemblies are defined as
stationary fluid zones. The cylindrical volumes are each defined as its
own individual fluid zone, so that a sliding mesh rotational speed may
be applied in Fluent®.

With the wind turbine geometry determined, the turbines are then
placed in various positions for analysis. Three different arrangements
of three turbines are simulated in this study. The first arrangement is
designed to determine the effects of wakes along a row of wind turbines.
The turbines are located 400 m apart and are aligned along the direction
of wind flow. The distance between these turbines corresponds to
approximately 5 rotor diameters, which is typical on a wind farm. This
arrangement can be seen in Figure 4 below.

Figure 4: Wind turbines arranged in a row (front view).

Two other arrangements are simulated in this study: 1) a triangular
arrangement and 2) a reversed triangular arrangement referred to as
the delta arrangement. Both of these arrangements are designed with various distances between the turbines in an attempt to determine
the impact the upstream turbine wakes have on the intake velocities
of the downstream turbines. The base case arrangement for both the
triangular and delta setups involves one turbine either 400 m upstream
or downstream of two turbines, with the two turbines placed 150 m to
either side of the single turbine. In the other cases, the downstream
distance between turbines is either increased to 500 m or 600 m and the
side to side distance of the two turbines is changed from 100 m to 200
m. Figures 5 and 6 shows an isometric view of both the triangular and
delta turbine arrangements.

Figure 5: Triangular 400-150 arrangement (isometric view).

Figure 6: Triangular 400-150 arrangement (front view).

In addition to the direct wind flow geometries, four geometries are
created to simulate variations in the incoming angle of the wind. This
is done by taking the base case of 400 m by 150 m and rotating the
turbines to face an incoming wind flow, which has been turned by a
given amount. Then all three turbines are rotated by the same amount
about the origin such that they face the inlet of the new geometry.
Using this modification, simulations can be conducted using the same
flow domain, with turbines interacting as if the incoming wind angle
had changed. In this study, both the delta and triangular cases have
geometries created for a five and ten degree angle of attack.

A grid sensitivity study, using the 400 by 150 m triangular
arrangement, found that decreasing the mesh size below 10 million
cells prevented solution convergence. The study also determined that
increasing the mesh size above 14 million cells yielded data that did
not differ much from the data obtained from k-ω SST simulations,
while drastically increasing the computational requirements for timely
solution convergence.

Validation

To ensure accurate prediction of airflow surrounding the rotating
wind turbine blades, simulations of the 0.66 m chord length S809
wind turbine airfoil experiencing wind flow similar to that at the tip
of a wind turbine blade were performed. To achieve validation of the
numerical results, a comparison was made with experimental results
obtained using a Reynolds number of 2,000,000 corresponding to
an inlet velocity of 52.28 m/s. Simulations were conducted at several
angles of attack relative to the wind direction. The data is compared to
experimental results obtained from the Delft University 1.8 m x 1.25
m low turbulence wind tunnel used by Wolfe and Ochs to validate
various CFD models of the S809 airfoil [24-26]. This brief comparison
ensures that the basic aerodynamic flow phenomena are accurately
represented in the CFD simulation. Figure 7 details the comparison
between experimental pressure data measured along the airfoil surface
and calculated pressure data from the CFD simulation.

In addition, measurements taken by Barthelmie et al. [27] were used
to validate the simulated velocity deficits generated by the wind turbine
wakes. Barthelmie et al. used a ship-mounted SODAR to measure wind
turbine wakes in an offshore farm in Denmark. The speed profile of the
operating turbines was measured and compared with meteorological
measurements from nearby masts. The farm contained Bonus Mk III
450 kW wind turbines with rotor diameters of 37 meters. In order to
validate the CFD model, a single turbine geometry of matched scale
was created.

As observed in Tables 1 and 2, the wake velocities calculated by
the CFD model in all cases is either within the error range of the sodar
measurements or very close to the range. Also noted by Barthelmie et al. is the fact that wakes meandering cause’s errors in the measured
data because only a partial wake is measured as opposed to a full wake.
Therefore, the CFD models should over-predict wake losses slightly.

Results

In total, 14 different turbine arrangements were simulated, with
three different velocities for each geometry (except in the altered wind
direction cases) to provide data over a broad spectrum of operating
conditions. The turbine row cases were designed to simulate what
should be avoided when designing a wind farm with a particular average
wind direction in mind. The first inlet velocity is set at the turbine
rated speed of 12 m/s with a rotational speed of 15 RPM decreasing
down the row. Figure 8 shows velocity contours along a cutting plane
viewed from the side, indicating the size and intensity of the wake as
it travels downstream. It is obvious from the contours that the wakes
experienced by downstream turbines increase in size and intensity as
air travels further downstream and encounters more turbines. This
view of the contours provides an easy method of visualizing wake size
and intensity. However, it does not provide specific information on the
losses experienced by the downstream turbines due to the wakes. Figure 9 provides a more quantitative view of the wind velocity as
the air travels downstream. The wind speed along the turbine group's
centerline shows the velocity deficits after each turbine in detail. The
first turbine experiences a wind speed of 12 m/s at the inlet, while the
second and third turbines experience wind speeds of approximately
10.5 m/s and 9.7 m/s, respectively. The equation for available wind
power is as follows,

Figure 8: Contours of velocity for the three turbines arranged in a row (12 m/s case).

Figure 9: Velocity along the turbine row centerline for the 12 m/s case.

Available wind power = 0.5×A×v3×ρ

Due to the cubic relationship between available wind power and
the wind velocity, a 1 m/s decrease in velocity from 10 m/s to 9 m/s
can result in an available power decrease of 25%. When examining
this simulation, it becomes increasingly clear why minimizing wake
losses in wind farms is essential to maintaining the efficiency of the
farm. Two additional simulations of this geometry were performed at
wind speeds of 10 m/s and 8 m/s. The behavior at these lower speeds
is almost identical to the behavior at 12 m/s. The observed velocities from all three cases indicate that the two downstream turbines produce
anywhere from 25 to 40% less power compared to the first turbine.

The first triangular geometry simulated was the 400 - 150 m case.
This geometry is used as a base case for both the triangular and delta
geometries simulated in this project. The cases were simulated at the
same three velocities as the three turbine row case: 12 m/s, 10 m/s, and 8
m/s. In this case, there is almost no wake interaction between turbines.
Each turbine should experience, at minimum, the inlet velocity of the
first turbine. Simulations were performed for both these arrangements
to determine if such arrangements might actually increase velocity at
the inlets of the downstream turbines, either due to a cascading effect
or the funneling of air flow.

Figure 10 shows the velocities at each turbine centerline. There is
a small but distinct increase in velocity at both downstream turbines.
Before the two turbines (green and blue lines), a 0.042 m/s increase in
velocity is observed. While this increase in velocity may appear to be small, the cubic relationship between available wind power and wind
speed shows that a 0.042 m/s increase in velocity at 12 m/s results in
a 1.05% improvement in performance at each downstream turbine,
or a 0.7% increase in energy production for the turbine group when
compared to the three individual turbines operating at the given speed.
For a group of three 1.5 MW turbines, a 0.7% performance increase
results in an additional 32,000 W of power. The 10 m/s and 8 m/s cases
result in similar, but smaller, velocity increases.

Figure 11, similar to Figure 10, shows the velocities at turbine
centerlines, with the velocity increase at the center turbine visible.
The delta cases were simulated to determine if the funneling of air
between two wakes could increase energy production. In this case, the
velocity increase occurs sooner than in the triangular case, and it is
higher, at about 0.061 m/s. While this velocity increase is higher than
the increase in speed due to the triangular arrangement, the percent
increase in performance for the whole group is lower, at about 0.5%. Similar results were observed for the delta cases when the wind speed
was reduced.

When the wind direction is changed, wake interactions become
much more significant. In fact, changes in wind direction completely
negate any performance gains from the arrangement of the turbines.
Therefore, in order to take maximum advantage of the arrangements
presented in this study, the wind farm site should be located in a region
with very little variability in wind direction. Figure 12 below shows an
example of the velocity contours generated by one of the four simulated
wind direction cases.

As seen in Figure 12, the left downstream turbine experiences a
waked flow at half of its rotor inlet speed, which leads to both reduced
power output from the turbine and additional fatigue stress due to the
varying velocities at the turbine inlet.

From the simulations, it was determined that, in general, the
triangular cases are more efficient than the delta arrangements at
corresponding velocities. Also, the triangular 400 m by 100 m geometry
produced the largest overall performance gains for the turbine group,
with the triangular case remaining slightly more effective at increasing
total power output than the delta case. The performance levels of the
turbine group geometries are shown in Figure 13 and Table 3 below.
The performance increases were determined by using the available wind power equation to calculate the percent increase in available
wind power at each turbine experiencing the velocity increase. The
power increases were then averaged over the group of three turbines to
determine the percent performance increase for the group as a whole,
and by extension, for a wind farm using the given arrangement.

As mentioned before, the 400 m by 100 m simulations showed
the largest performance gains compared to turbines experiencing the
given speeds individually or without influence from a grouping, such
as ones in a parallel row. The four simulations conducted with various
wind directions indicated that the benefits of the triangular or delta
arrangements are most pronounced when the wind travels directly
downstream. If the wind direction changes roughly 10 to 15º at a
given site, the 400 by 150 m cases can cause certain turbines to become
waked, resulting in the negation of any performance improvements
due to the geometry.

Conclusion

This study proposes a possible method of generating more power
from wind turbines by arranging turbines in either triangular or delta
groups, arrangements designed to increase wind flow at rotor inlet
planes by either cascading flow around a single leading turbine or by
funneling it through the area between two turbine wakes. To investigate
the appropriateness of each arrangement, several CFD simulations of various turbine geometries were performed. Each geometric variation
was simulated at three different velocities at the domain inlet (12 m/s,
10 m/s, and 8 m/s) to simulate the various wind speeds that might be
encountered by turbines operating in a farm. In addition, four extra
simulations were performed to determine the effects of wind direction.

The results of this study indicate that the triangular arrangements
produce more energy than the delta arrangements. This is primarily
due to the increase in velocity at the two rear turbines in the triangular
arrangement, as opposed to an increase in velocity at only a single rear
turbine in the delta cases. Of all the arrangements, the 400 m by 100
m triangular arrangement yielded the best results, with a performance
increase of 1.05%, which could lead to an additional 47,000 W of
power. Theoretically, in a utility scale wind farm capable of producing
200 MW of power, this performance increase applied to the entire farm
would result in an increase in power generation about of 2.1 MW. If the
given 200 MW wind farm has an installation cost of $100,000,000, the
cost per MW of energy production capacity at installation is $500,000.
Using the triangular groupings, the power production capacity would
increase to 202.1 MW, resulting in a cost per MW value of about
$494,070. Therefore, through the use of the triangular arrangement,
the initial cost per MW of power generation capacity is reduced by
approximately 1.1%. In the case described above, this translates to an
overall savings of $6000 saved per MW of capacity installed.

However, this performance increase is not without certain
drawbacks. Since the turbines are placed relatively close together, the
possibility of intense turbulence from wake interactions is significantly
higher. Also, in sites where the wind shifts direction frequently, the
benefits of the triangular arrangement are significantly diminished. In
fact, additional maintenance costs might be incurred if certain wind
directions result in the upstream turbine directly waking one of the
downstream turbines. Finally, all simulations were performed with the
assumption that the turbines sat on completely level ground, such as a
large field with few trees or an offshore farm. Therefore, the results may
have little bearing on sites when terrain obstructions are present. In
summary, these arrangements are recommended for use in utility scale
farms only when the average annual wind direction is fairly consistent
and the land is relatively level.

Acknowledgements

This research was supported in part by US Department of Energy Grant DEEE0003265
and US Department of Education Grant P116B100322. However,
the contents do not necessarily represent the policy of the U.S. Department of
Education, and endorsement by the Federal Government should not be assumed.